Steane code

The Steane code is a tool in quantum error correction introduced by Andrew Steane in 1996. It is a perfect CSS code (Calderbank-Shor-Steane), using the classical binary Hamming code to correct for qubit flip errors (X errors) and the dual of the Hamming code, the code, to correct for phase flip errors (Z errors). The Steane code is able to correct arbitrary single qubit errors. The Steane code is a tool in quantum error correction introduced by Andrew Steane in 1996. It is a perfect CSS code (Calderbank-Shor-Steane), using the classical binary Hamming code to correct for qubit flip errors (X errors) and the dual of the Hamming code, the code, to correct for phase flip errors (Z errors). The Steane code is able to correct arbitrary single qubit errors. In the stabilizer formalism, the Steane code has 6 generators, and the check matrix in standard form is where H is the parity-check matrix of the Hamming code and is given by The [ [ 7 , 1 , 3 ] ] {displaystyle ]} Steane code is the first in the family of quantum Hamming codes, codes with parameters [ [ 2 r − 1 , 2 r − 1 − 2 r , 3 ] ] {displaystyle ]} for integers r ≥ 3 {displaystyle rgeq 3} . It is also a quantum color code.